U.S. patent number 9,608,317 [Application Number 14/312,360] was granted by the patent office on 2017-03-28 for system, method and apparatus including hybrid spiral antenna.
This patent grant is currently assigned to Trustees of Tufts College. The grantee listed for this patent is Mohammed N. Afsar, Nahid Rahman. Invention is credited to Mohammed N. Afsar, Nahid Rahman.
United States Patent |
9,608,317 |
Rahman , et al. |
March 28, 2017 |
System, method and apparatus including hybrid spiral antenna
Abstract
A spiral antenna device includes a plurality of generally
polygonal loops. The polygonal loops have respective side counts
that decrease progressively as a function of the loop's radial
distance from a center of the antenna device. The side count may
vary between loops as a multiple of a power of two.
Inventors: |
Rahman; Nahid (Rupnagar,
BD), Afsar; Mohammed N. (Somerville, MA) |
Applicant: |
Name |
City |
State |
Country |
Type |
Rahman; Nahid
Afsar; Mohammed N. |
Rupnagar
Somerville |
N/A
MA |
BD
US |
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Assignee: |
Trustees of Tufts College
(Medford, MA)
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Family
ID: |
48669573 |
Appl.
No.: |
14/312,360 |
Filed: |
June 23, 2014 |
Prior Publication Data
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Document
Identifier |
Publication Date |
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US 20140300526 A1 |
Oct 9, 2014 |
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Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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PCT/US2012/071422 |
Dec 21, 2012 |
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61630987 |
Dec 23, 2011 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
H01Q
21/00 (20130101); H01Q 1/36 (20130101); H01Q
7/00 (20130101); H01Q 9/27 (20130101) |
Current International
Class: |
H01Q
1/36 (20060101); H01Q 7/00 (20060101); H01Q
21/00 (20060101); H01Q 9/27 (20060101) |
Field of
Search: |
;343/867,866,895 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
Other References
Lipsky, Stephen E., Antenna Elements for Microwave Passive
Direction Finding, Microwave Passive Direction Finding, SciTech
Publishing, pp. 36-67, 1987. cited by applicant .
Caswell, Eric D., Design and Analysis of Star Spiral With
Application to Wide Band Arrays With Variable Element Sizes.
Digital Library an Archives, University Libraires, Virginia Tech,
pp. 75-126, 2001. cited by applicant .
Kramer, Brad A., et al., Design and Performance of an
Ultrawide-Band Ceramic-Loaded Slot Spiral, IEEE Transactions on
Antennas and Propagation, vol. 53, No. 7, pp. 2193-2194, Jul. 2004.
cited by applicant .
Balanis, Constantine A., Aperature Antennas, Antenna Theory:
Analysis Design, 3.sup.rd Edition, John Wiley & Sons, Inc., pp.
653-738, 2005. cited by applicant .
Gustafsson, Mats, Broadband array antennas using a
self-complementary antenna array and dielectric slabs, Technical
Report LUTEDX/(TEAT-7129)/1-8/(2004), 1-8. cited by applicant .
Saynak, Ugur and Kustepeli, ALP, Novel Square Spiral Antennas for
Broadband Application, Frequez 63, 1-2, pp. 14-19, 2009. cited by
applicant .
Palreddy, Sandeep and Cheung, Rudolf, Two-arm Archimedean Spiral
Helical Antenna with Wraparound Absorber, 25.sup.th Annual Review
of Progress in Applied Computational Electromagnetics, ACES, 6pp,
2009. cited by applicant .
Rahman, Nahid, et al., Characterization, Design and Optimization of
Low-Profile Cavities for UWB Spiral Antennas, International Journal
of Electromagnetics and Applications, 2(3), pp. 16-23, 2012. cited
by applicant .
Nakano, Hisamatsu, Helical and Spiral Antennas, Encyclopedia of
Telecommunications, John Wiley & Sons, Inc., published online
Apr. 15, 2003, http://dx.doi.org/10.1002/0471219282.eot235. cited
by applicant .
Navarro, Julio A., Spatial and Quasi-Optical Power Combining.
Encyclopedia of RF and Microwave Engineering, pp. 4837-4879,
published online Apr. 15, 2005. cited by applicant .
Antenna Magus,
http://www.antennamagus.com/database/antennas/antenna.sub.--page.php?id=9-
5. cited by applicant.
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Primary Examiner: Levi; Dameon E
Assistant Examiner: Davis; Walter
Attorney, Agent or Firm: Bergman & Song LLP Bergman;
Michael
Parent Case Text
CROSS-REFERENCE TO RELATED APPLICATIONS
The present application is a Continuation of PCT application number
PCT/US2012/071422 having an international filing date of Dec. 21,
2012 the disclosure of which is herewith incorporated by reference
in its entirety, which in turn claims the benefit of U.S.
provisional patent application No. 61/630,987, filed on Dec. 23,
2011, the disclosure of which is herewith incorporated by reference
in its entirety.
Claims
The invention claimed is:
1. A wideband antenna comprising: a first conductor having a first
end, a second end, a first longitudinal surface disposed between
said first end and said second end, and a first longitudinal axis,
said first longitudinal axis defining at least first and second
polygonal spiral loops said first and second polygonal spiral loops
being signalingly coupled to one another in series, said second
polygonal spiral loop being disposed radially outward of said first
polygonal spiral loop, said first polygonal spiral loop having a
first plurality of segments and a first segment count, said second
polygonal spiral loop having a second plurality of segments and a
second segment count, said second segment count being less than
said first segment count and said first and second segment counts
being numerically related as an integer power of two.
2. A wideband antenna as defined in claim 1 wherein respective
lengths of said first plurality of segments are all approximately
equal to one another.
3. A wideband antenna as defined in claim 1 further comprising a
second conductor, said second conductor being geometrically similar
to said first conductor, said second conductor being interleaved
with said first conductor.
4. A wideband antenna as defined in claim 1 wherein a spiral loop
of said second conductor is substantially coaxial to said first
spiral loop of said first conductor within a mutual plane of said
first and second conductors.
5. A wideband antenna as defined in claim 1 wherein said second
conductor is oriented at a rotation of approximately 180.degree.
with respect to said first conductor within a mutual plane of said
first and second conductors.
6. A wideband antenna as defined in claim 1 wherein each segment of
said first and second plurality of segments has a respective
segment length and wherein said respective segment lengths increase
substantially monotonically between said first end and said second
end.
7. A wideband antenna as defined in claim 1 wherein each of said
segments of said first and second pluralities of segments has
respective endpoints defined by parametric equations of
r'=ae/cos(de/2), x=r' cos(e) and y=r' sin(e).
8. A wideband antenna as defined in claim 1 wherein each of said
segments of said first and second pluralities of segments is
disposed substantially tangent to a geometric spiral.
9. A wideband antenna as defined in claim 8 wherein said geometric
spiral includes an Archimedean spiral.
10. A wideband antenna as defined in claim 1 further comprising: a
further conductor having a further polygonal spiral loop disposed
in spaced relation to said second polygonal spiral loop to form an
antenna array, wherein a spacing between respective centers of said
second polygonal spiral loop and further polygonal spiral loop
exceeds a sum of the respective radii of said second and further
polygonal spiral loops.
11. A spiral antenna comprising: a piecewise linear spiral member
including a plurality of longitudinal regions disposed adjacent to
one another at a respective plurality of vertices, said plurality
of vertices having respective angular measures diminishing
monotonically from an innermost vertex to an outermost vertex of
said spiral along a longitudinal axis of said linear spiral
member.
12. A spiral antenna as defined in claim 11 wherein a smallest
vertex of said plurality of vertices has an angular dimension of at
least about 90.degree..
13. A spiral antenna as defined in claim 11 wherein a largest
vertex of said plurality of vertices has an angular dimension of at
most about 179.degree..
14. A spiral antenna as defined in claim 11 wherein said plurality
of longitudinal regions defines at least one polygonal loop having
sides of approximately equal length and wherein said plurality of
longitudinal regions defines at least one interpolated polygonal
loop having sides of substantially different lengths.
15. A spiral antenna as defined in claim 11, further comprising a
curved spiral member electrically coupled to said piecewise linear
spiral member.
16. A spiral antenna as defined in claim 11 wherein said plurality
of longitudinal regions defines at least a first loop and a second
loop, said first loop having a number of sides taken over
360.degree. related as a power of 2 to a number of sides taken over
360.degree. of said second loop.
17. A method of communicating comprising: stimulating an electronic
signal in a spiral antenna, said spiral antenna including a
generally spiral longitudinal member, said generally spiral
longitudinal member including a first region describing an
approximately rectangular polygonal spiral and a second region
describing an approximately non-rectangular polygonal spiral,
wherein said second region approximates a polygon having a number
of sides, said number of sides equal to two raised to a power of
two.
18. A method of communicating as defined in claim 17 wherein said
second region is disposed inwardly of said first region.
19. A method of communicating as defined in claim 17 wherein said
first and second regions are disposed substantially coplanar to one
another.
20. A method of communicating as defined in claim 17 wherein said
spiral antenna comprises a substantially electrically conducting
material.
21. A method of communicating as defined in claim 20 wherein said
substantially electrically conducting material comprises at least
one of copper, aluminum, silver, and gold.
22. A method of communicating as defined in claim 17 wherein said
spiral antenna comprises an Electromagnetic Bandgap material.
23. A method of communicating as defined in claim 17 wherein said
spiral antenna comprises a meta material.
24. A method of communicating as defined in claim 17 wherein said
first region has a further number of sides, said further number of
sides being equal to two raised to a further power of two, said
first and second powers of two differing by an integer value of at
least two.
Description
FIELD OF THE INVENTION
The present invention relates to electromagnetic radiation, and
more particularly to apparatus and methods for coupling an
electronic device to an electromagnetic field.
BACKGROUND
Various devices, known generally as antennas, are advantageously
employ to couple an electronic device to a time varying
electromagnetic field. In diverse applications, antennas are used
to couple power into and out of an electromagnetic field and to
transmit and receive signalingly modulated electromagnetic fields.
Circular spiral antennas have been used in a number of such
applications. They are desirable for, among other characteristics,
the production of circularly polarized electromagnetic radiation. A
circularly polarized receiving antenna will receive a portion of an
incoming signal regardless of the spatial orientation of the
receiving antenna. Consequently, circular polarization is used
extensively in communications applications where an orientation of
a transmitting or receiving antenna may be altered in a way that is
unpredictable or otherwise undesirable. For example, systems for
communicating with orbiting and extra-orbital spacecraft typically
employ circular polarization.
A square spiral antenna is a known variant of a circular spiral
antenna. Square spiral antennas have certain advantages over
circular spiral antennas. These advantages are particularly evident
with respect to relatively low frequencies of electromagnetic
radiation.
Notwithstanding their long use and well understood theory, circular
and square spiral antennas exhibit deficiencies for which no
satisfactory remedy has previously been presented. The
corresponding long-felt, but unsatisfied need for improved devices
is at last addressed in the substance of the present disclosure.
Indeed, the present invention emerges from new insights and
understanding of these deficiencies developed by the present
inventors and reflected in the novelty of the corresponding
inventions.
SUMMARY
Having thus examined and understood a range of previously available
devices, the inventors of the present invention have developed a
new and important understanding of the problems associated with the
prior art and, out of this novel understanding, have developed new
and useful solutions and improved devices, including solutions and
devices yielding surprising and beneficial results.
The invention encompassing these new and useful solutions and
improved devices is described below in its various aspects with
reference to several exemplary embodiments including a preferred
embodiment.
Planar Archimedean spiral antennas are most often designed to
operate in two principal configurations, i.e. circular and
rectangular. Based on the requirements of a specific application,
both configurations have their advantages and disadvantages. For
instance, square spirals have the advantage of operating with
similar gain performance at lower frequencies than their circular
counterparts.
In accordance with the current band theory, the first radiation
band of a spiral antenna occurs when the circumference of the
spiral is one current wavelength at the operating frequency. This
circumference corresponds to: D=.lamda..sub.e/.pi. 1) for the
circular case, where D is diameter and .lamda..sub.e is effective
wavelength and, for the square case: W=.lamda..sub.e/4 2) where W
is the side length of the square and where .lamda..sub.e is the
effective wavelength. Therefore, the first operating frequency is
approximately 22% lower for a square spiral than that of a circular
one when they both have the same diameter. This means that for a
given frequency, the first radiation mode of a square spiral
antenna will occur at a smaller radius than for the corresponding
circular spiral allowing for better utilization of available
aperture. The longer circumference of square spirals provide an
inherent miniaturization factor MF=4/.pi.. Consequently, square
spiral antennas can be packaged closer together than circular
spirals in an array configuration when constrained to the same
space or whenever a square mounting footprint is required.
The fundamental advantage, however, of using spiral antenna systems
is the radiation of circularly polarized waves over ultra-wide
bandwidths. Although square spirals allow for compact packaging,
they often demonstrate irregular performance across the band and
commonly have poor axial ratio performance compared to their
circular Archimedean counterparts. A commonly accepted figure of
merit for circularly polarized antennas (antennas can be either
circular or rectangular spiral antennas) is that their axial ratios
should remain below 3 dB across their entire frequency range of
operation.
In recent work, modified logarithmic and modified hybrid
rectangular geometries have been proposed to improve the
performance of conventional square Archimedean spirals. Such
devices, however, generally have axial ratios greater than 4 dB
over a significant portion of their operational bandwidths. In
other work, the use of high-contrast dielectric materials in slot
spirals has been shown to improve the axial ratio to some extent at
ultra high frequencies (UHF: 0.5-2 GHz). The above-noted
deterioration of axial ratio for square spirals operating at ultra
wideband (UWB) frequencies, (i.e. UWB: 2-18 GHz) is effectively
overcome by various antennas prepared according to principles of
the present invention, while maintaining the advantages of the
square spiral.
One of the several exemplary embodiments and variants of the
present invention presented below is a wideband spiral antenna
having a 16 turn generally polygonal spiral structure. The
structure includes innermost loops with 32 sides each, as well as
four additional loops having 16 sides each. In addition the
structure includes four further loops of eight sides each and
another four outermost loops having four sides each.
Of course, it will be understood that the corresponding spiral slot
antenna would also fall within the scope of the invention. Such
antenna includes, as an example, an electrically conductive body
member, such as a copper plate, having first and second
substantially planar surfaces, i.e., flat sides disposed
substantially parallel to one another. Polygonal spiral slots
through the copper plate are arranged in loops like those described
immediately above to form radiating spiral apertures.
The slots or members (depending on the embodiment) are arranged in
an Archimedean spiral, or in a modified Archimedean spiral
according to the requirements of a particular embodiment. As will
be discussed in additional detail below, the loops may include
interpolated loops, including single interpolated loops and/or a
progression of interpolated loops providing a transition between
polygonal spiral loops of different configurations. In one
exemplary embodiment, an overall linear dimension of about 2 inches
characterizes a spiral antenna according to the invention. Antennas
having a wide variety of other dimensions are also contemplated. In
other embodiments, a plurality of such antennas forms an array.
One of skill in the art will anticipate a wide variety of
performance characteristics according to the particular dimensions
and features of corresponding embodiments. That said, certain
embodiments of the invention can be expected to exhibit a radiating
bandwidth from at least about 2 GHz to at least about 18 GHz.
Likewise, certain embodiments of the invention can be expected to
exhibit an axial ratio over such a radiating bandwidth of at most
about 3.5 dB, and in some cases less than 3 dB over most of the
radiating bandwidth. Similarly, a voltage standing wave ratio
(VSWR) over the radiating bandwidth of at most about 2.5 can be
anticipated.
While different embodiments will exhibit a corresponding variety of
input impedance characteristics, preparing an antenna having an
input impedance of about 188.OMEGA. will be within the skill of the
ordinary practitioner in light of the present disclosure. In
addition, the practitioner of ordinary skill in the art will
appreciate that providing an absorbing cavity or other absorbing
device proximate to one face of the spiral will substantially limit
an effective transmission or reception lobe to the opposite side of
the spiral.
These and other advantages and features of the invention will be
more readily understood in relation to the following detailed
description of the invention, which is provided in conjunction with
the accompanying drawings.
It should be noted that, while the various figures show respective
aspects of the invention, no one figure is intended to show the
entire invention. Rather, the figures together illustrate the
invention in its various aspects and principles. As such, it should
not be presumed that any particular figure is exclusively related
to a discrete aspect or species of the invention. To the contrary,
one of skill in the art would appreciate that the figures taken
together reflect various embodiments exemplifying the
invention.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1A shows, in schematic perspective view, a circular spiral
antenna device prepared according to a design of the present
inventors;
FIG. 1B shows, in schematic perspective view, a square spiral
antenna device prepared according to a design of the present
inventors;
FIG. 2 shows, in schematic perspective view, a hybrid polygonal
antenna device prepared according to principles of the
invention;
FIG. 3A shows a geometric spiral having characteristics associated
with an antenna device prepared according to principles of the
invention;
FIG. 3B illustrates design steps related to preparing an exemplary
antenna device according to principles of the invention;
FIG. 4 shows a portion of a geometric spiral illustrating analysis
of corresponding parametric equations;
FIG. 5A shows a generally circular geometric spiral;
FIG. 5B shows a generally rectangular geometric spiral;
FIG. 6 shows a polygonal geometric curve illustrating certain
characteristics of a hybrid polygonal antenna device like that of
FIG. 2;
FIG. 7A shows, in schematic perspective view, a hybrid polygonal
antenna device prepared according to principles of the
invention;
FIG. 7B shows a geometric spiral having characteristics associated
with an antenna device prepared according to principles of the
invention;
FIG. 8A shows, in schematic perspective view, a hybrid polygonal
antenna device including an interpolated loop prepared according to
principles of the invention;
FIG. 8B shows a geometric spiral having characteristics associated
with an antenna device including an interpolated loop prepared
according to principles of the invention;
FIG. 9A shows, in schematic perspective view, a hybrid polygonal
antenna device including an interpolated loop prepared according to
principles of the invention;
FIG. 9B shows a geometric spiral having characteristics associated
with an antenna device including an interpolated loop prepared
according to principles of the invention;
FIG. 10 shows several geometric spirals showing the arrangement of
a portion of an antenna array including polygonal spirals according
to principles of the invention;
FIG. 11 shows a schematic cross-section of a portion of an antenna
according to principals of the invention;
FIG. 12 shows a plot of axial ratio as a function of frequency
representing simulated performance of an antenna prepared according
to principles of the invention;
FIG. 13 shows a plot of VSWR as a function of frequency
representing simulated performance of an antenna prepared according
to principles of the invention;
FIG. 14 shows a plot of input impedance as a function of frequency
representing simulated performance of an antenna prepared according
to principles of the invention;
FIG. 15 shows a plot of S11 as a function of frequency representing
simulated performance of an antenna prepared according to
principles of the invention;
FIG. 16 shows a schematic representation of in-phase and
out-of-phase current regions representing simulated performance of
an antenna prepared according to principles of the invention;
FIG. 17 shows a further aspect of the invention, in cutaway
perspective view, including a portion of a helical spiral antenna
device; and
FIG. 18 shows a further aspect of the invention, in cutaway
perspective view, including a portion of a helical spiral antenna
with coplanar symmetrical loops.
DETAILED DESCRIPTION
The following description is provided to enable any person skilled
in the art to make and use the disclosed inventions and sets forth
the best modes presently contemplated by the inventors of carrying
out their inventions. In the following description, for purposes of
explanation, many specific details are set forth in order to
provide a thorough understanding of the present invention. It will
be apparent, however, to one skilled in the art that the present
invention may be practiced without these specific details. In other
instances, well-known structures and devices are shown in block
diagram form in order to avoid unnecessarily obscuring the
substance disclosed.
The present invention relates to a system, apparatus and method for
producing electromagnetic radiation, including an antenna device
having a generally spiral aspect. Certain embodiments of a device
prepared according to principles of the invention include a
modified polygonal Archimedean spiral antenna well adapted to
radiate in a 2-18 GHz bandwidth. Also disclosed is a spiral antenna
having performance which approximates a circular spiral antenna
(like that shown 100 in FIG. 1A) in its highest frequencies of
operation. The spiral antenna further exhibits performance that
gradually transitions to approximate that of a square spiral
antenna (like that shown 102 in FIG. 1B) at its lowest frequencies
of operation. Among other advantages, a device prepared according
to the present invention is well adapted to produce circularly
polarized waves over ultra-wide bandwidths while embodying
low-profile geometries for efficient array packing.
It is well-known that self-complementary structures tend to have a
constant input impedance and hence are good candidates for
ultra-wideband antennas. Among the advantages of the invention
described herewith, many embodiments of antennas prepared according
to principles of the invention are substantially
self-complementary.
FIG. 2 shows an exemplary two-arm, 16 turn spiral antenna device
200 prepared according to principles of the invention. The
illustrated device, includes a substrate member 202 having a
substantially planar support surface 204. In a typical embodiment,
the substrate member 202 includes material having a substantially
electrically insulating characteristic. In some embodiments, the
substrate member includes material having the characteristics of an
electrical semiconductor. In certain embodiments, the substrate
member includes a polymer foam having material constitutive
properties (permittivity and permeability) similar to air. For
example, one might use Emerson and Cuming.RTM. ECCOSTOCK.RTM.PP,
which is a closed cell, cross-linked hydrocarbon foam with low
dielectric loss, low dielectric constant, and low density. This
foam is light-weight, weather resistant and has negligible water
absorption and provides excellent thermal insulation. The
dielectric constant does not change with frequency and any change
with temperature is negligible. One of skill in the art will
understand that other similar materials may be employed.
First 206 and second 208 spiral arms have respective original ends
210, 212 proximate to a normal central axis 214 of the support
surface 204. In addition, the spiral arms 206, 208 have further
respective terminal ends 216, 218 comparatively distal to the
normal central axis 214. Between the respective original ends 210,
212 and terminal ends 216, 218, each spiral arm describes a
generally polygonal spiral wherein radially adjacent loops, e.g.
220, 222 of one arm are disposed substantially co-axial to one
another about central axis 214.
In the illustrated embodiment, an absorbing device 224 is disposed
in proximity to substrate member 202 and adjacent to a reverse side
of the substrate, taken with respect to support surface 204. In
other embodiments, the absorbing device 224 is integral to
substrate member 202. As will be understood by one of ordinary
skill in the art, the absorbing device serves to substantially
absorb and prevent the radiation of a rear primary lobe by the
spiral antenna device 200.
In the illustrated embodiment, the antenna device 200 is
substantially square and has an overall linear dimension 226 of
approximately 2 inches. One of skill in the art will appreciate,
however, that other dimensions and configurations are possible
according to the requirements (e.g., desired radiation wavelength
band) of a particular application. In particular, in certain
embodiments it will be advantageous to employ an Electromagnetic
Band Gap (EBG) material and/or a metamaterial such as is known, or
may be developed, in the art in proximity to the spiral device.
In certain embodiments, the absorbing device 224 includes a
shallow, multi-layer absorptive cavity with three constituent
commercially available absorbing materials. In this demonstration,
a front layer at the air-absorber interface (AN series, Emerson and
Cumming) includes a carbon-loaded polyurethane foam absorber. A
second layer (LS-10055, ARC technologies) includes a flexible,
low-density and high loss carbon loaded foam. A metal-backed
3.sup.rd layer includes an iron-loaded, magnetic thermoplastic
elastomer (WT-BPJA-010, ARC technologies. The illustrated
embodiment, according to principles of the invention, includes a
cavity depth 228 that ensures 2-18 GHz absorption for maximum
gain-bandwidth performance. In certain embodiments, depth 228 is at
least about 0.625 inch, including an air-gap between the radiator
and the absorbing layers. The cavity is used for unidirectional
operation of the spiral antenna and the constituent materials and
cavity depth can be adjusted according to application
requirements.
FIG. 3 shows a geometric curve 300 similar to that described by one
arm of the spiral antenna device 200 of FIG. 2. The curve is
piecewise linear between an inner original end 310 and an outer
terminal end 316. A first substantially linear segment 318 is
disposed between outer terminal end 316 and a first vertex 320. The
first vertex 320 of the illustrated exemplary curve has an angular
dimension substantially equal to 90.degree.. A second substantially
linear segment 322 is disposed between first vertex 320 and a
second vertex 324 which also has an angular dimension substantially
equal to 90.degree.. A third substantially linear segment 326 is
disposed between second vertex 324 and a third vertex 328 which
also has an angular dimension substantially equal to 90.degree.;
and a fourth substantially linear segment 330 is disposed between
third vertex 328 and a fourth vertex 332. Together, the first 318,
second 322, third 326 and fourth 330 substantially linear segments
form an outermost loop 334. The outermost loop 334 is regarded as
substantially polygonal and, in this case, substantially square
because each of vertices 320, 324, 328 and 332 has an angular
dimension substantially equal to 90.degree..
It should be noted that loop 334 is not precisely polygonal,
because the respective lengths of the substantially linear segments
diminish monotonically between terminal end 316 and vertex 332. For
purposes of this application, the term monotonic is intended to
refer to a series of values which either remain equal or change in
only one sense (i.e., decrease or increase) from value to value
through the series. For example, the sequence 10, 9, 8, 8, 8, 6, 5,
4, 4, 4, 3, 0, -7 is considered to be monotonically decreasing.
This sequential diminution of segment length results in a radial
offset 336 between vertex 332 and terminal end 316, and in a
corresponding gap 338 between successive polygonal loops (e.g.,
between first polygonal loop 334 and a second polygonal loop 340).
Nevertheless, for purposes of this disclosure and as noted above,
loop 334 is considered to be substantially polygonal.
The region of gap 338 defined between first linear segment 318 and
a fifth linear segment 342 is generally rectangular in form. Other
regions of the gap will have other configurations, however. For
example, the gap 338 is generally triangular at region 344.
Like loop 334, loop 340 may be considered substantially square for
purposes of the present application. Similarly, loops 345 and 346
are considered to be substantially square for purposes of the
application, and all of loops 334, 340, 345 and 346 are considered
to be substantially concentric with respect to each other about a
centerpoint 348 of the spiral.
It is worth noting that, where a particular antenna device of the
invention has more than one arm, the spiral arms are generally
interleaved with one another. Accordingly, a second spiral arm
would embody a geometric curve substantially similar in
configuration to curve 300. The second spiral arm would be disposed
within gap 338 and substantially concentric with spiral 300 about
centerpoint 348. Such an arm would divide gap 348 and thus define
additional gaps in which still further arms might be disposed,
where appropriate. In certain embodiments, the second spiral arm
would be disposed such that a linear segment of the second spiral
arm would be disposed substantially equidistant between adjacent
segments of the first spiral arm. In certain embodiments, the
spiral arm is disposed in an orientation that is rotated in the
plane of the spiral by approximately 180.degree. with respect to
the first spiral arm.
It should also be noted that each of loops 334, 340, 345 and 346 is
considered to be substantially square in the illustrated
embodiment. Curve 300 includes additional loops 350, 352, 354 and
356, which for purposes of the present disclosure are deemed to be
substantially octagonal. Accordingly, curve 300 maybe regarded as
having groups of loops 358, 360, 362 and 364; the loops of group
358 being four-sided (i.e., substantially square), the loops of
group 360 being eight-sided (i.e., substantially octagonal), the
loops of group 362 being 16-sided and the loops of group 364 being
32-sided.
In the illustrated embodiment, the number of sides of the groups
are related by powers of 2. Thus, whereas each loop of the
outermost group 358 has four sides (2 exponent 2), each loop of
group 360 has eight sides (2 exponent 3), each loop of group 362
has 16 sides (2 exponent 4), and each loop of group 364 has 32
sides (2 exponent 5).
FIG. 3B illustrates a graphical method 390 for arriving at this
mathematical progression by truncating a related polygon at its
vertices, beginning with a square 392. Truncating the corners of
the square 392 results in an octagon 394, which may be similarly
modified to produce a 16 sided polygon 396. Further modification of
the 16 sided polygon 396 produces a 32 sided polygon 398.
A further notable aspect of exemplary curve 300 is that, while the
vertices within a group are substantially radially aligned with one
another, the vertices of adjacent groups are offset from one
another. Thus vertices 328, 366, 368 and 370 are substantially
radially aligned along radial axis 372. Likewise, vertices 374,
376, 378 and 380 are substantially radially aligned along radial
axis 382. Axes 372 and 382 are not, however, aligned but are
disposed at an oblique angle with respect to one another.
The reader will note that, while radial alignment of all vertices
within a group is found in certain devices prepared according to
the invention, it is absent from other embodiments of the
invention. For example, FIGS. 7A, 8A and 9A (discussed below) show
further devices prepared according to principles of the invention
without the substantial radial alignment of group vertices found in
curve 300.
Referring again to FIG. 3 and considering curve 300 more
analytically, the Archimedean spiral curve is defined by the polar
equation: r=a*.theta., where .theta..gtoreq.0. 3) The system of
parametric equations corresponding to the polar curve is:
x=a.theta. cos(.theta.) and 4) y=a.theta. sin(.theta.), 5) where a
is any real number denoting the growth rate of the spiral.
For the polygonal spiral case, when one increases the angle
d.theta. to construct a next group of polygons with half the number
of sides of the previous group, if the radius is not appropriately
adjusted, the inner polygons will intersect with the outer polygons
at some distance along the curve. To correct for the distance
between adjacent sides and to ensure that the linear end portion of
the next turn of the spiral does not come any nearer than the
vertex of the previous side, the parametric equations are modified
as: r'=a.theta./cos(d.theta./2),x=r' cos(.theta.) and 6) y=r'
sin(.theta.). 7) In this way, since cos(d.theta./2) is always
.ltoreq.1, the radius is modified to be slightly larger than the
true Archimedean spiral as shown in FIG. 4.
In order to create a particular polygonal loop, the angle of
rotation to create the sides is determined from:
d.theta.=(2.times..pi.)/(# of sides) 8) where d.theta. is the angle
of rotation.
When making a transition from a group of 2.sup.n sided polygons to
2.sup.n-1 sided polygons, one may choose to make either the flat
sides of different polygons parallel to each other or make the
vertices group of an inner set of polygons line up with the
vertices and centers of an outer group of polygons. The former
reduces the irregularity in the transition from 2.sup.n side
polygon to 2.sup.n-1 sided polygon and best preserves the
self-complimentary form of the two-arm spiral. Hence, to ensure a
substantially symmetric spiral polygonal structure, with regular
transitions from 2.sup.n to 2.sup.n-1 sides, the flat sides are
preferably designed parallel and centered about the next larger
group of sides. Curve 300 of FIG. 3A exemplifies these
characteristics.
Reference is now made to FIGS. 5A and 5B and to respective
idealized spiral antennas 500 and 550. Without intending to be
bound to a particular theory of operation, the inventors offer the
following observations. According to the current band theory for
planar Archimedean spiral antennas, when the total circumferential
path length is .lamda..sub.e, where .lamda..sub.e is the effective
wavelength or current wavelength, the current at A (e.g., 502) and
the current at its neighboring point B' (e.g., 504) on the adjacent
arm are in phase. Similarly, the current at B (e.g., 506) and the
current at its neighboring point A' (e.g., 508) on the adjacent arm
are in phase. FIGS. 5A and 5B illustrate these four currents at
points A, B', B, and A', where each pair of currents forms a band
of current.
Spiral antennas follow the principles of a slow-wave structure. The
two current bands in FIGS. 5A and 5B rotate around the center-point
o (e.g., 510) with time. Consequently the electric field radiated
from each current band also rotates. Therefore, the radiation field
is circularly polarized.
For every differential group of elements that have shifted 180
degrees in phase at the diameter of radiation, there is another
group that is in time and space quadrature (of equal amplitude and
90.degree. out of phase) since the phase of the groups varies as a
function of the spiral growth rate. This causes a 90 degree phase
shift making the spiral response circular.
FIG. 6 shows a further aspect of an idealized spiral antenna 600
according to principles of the invention. Antenna 600 incorporates
two interleaved piecewise-linear curves 602 and 604, each being
substantially similar to curve 300 of FIG. 3. Accordingly, curves
602 and 604 are substantially similar to one another, and are
displaced from one another by a rotation of approximately
180.degree. in the plane of the image.
Curve 604 has an original end 606 disposed proximate to a
centerpoint 608 and a terminal end 610 relatively radially distant
from the centerpoint. In like fashion, curve 602 has an original
end 612 and a terminal end 614. Progressing outwardly from the
origin along curve 602, one reaches, for example, a transition
point 616 where vertex 618 of curve 604 is not matched by a
corresponding vertex of curve 602. Rather, curve 602 proceeds in
linear fashion to vertex 620, thereby affecting a transition from
an octagonal loop to a square loop.
180.degree. away from transition 616, curve 604 effects a similar
transition 622. Instead of matching vertex 624 of curve 602, curve
604 proceeds straight to vertex 626 and transitions, from an
octagonal loop to a square loop. Depending on the arrangement of a
particular antenna, additional transition points will be found
wherever loops transition from one polygonal configuration to
another. Thus, for example, additional transition points are found
in curves 602 and 604 at locations 628 and 630 respectively.
In the illustrated polygonal spiral antenna 600, and others of the
present invention, as the two current bands are rotating with time,
when the effective wavelength is such that the current band or the
same phase currents between the adjacent arms reaches a point where
one arm is transitioning the antenna geometry from a 2.sup.n side
polygon to a to a 2.sup.n-1 side polygon, while the other arm
remains in a 2.sup.n sided polygonal turn, the currents are no
longer in phase in the vicinity of the transition point.
Furthermore, another differential group of currents in phase
quadrature may not be available. This absence or diminution of
currents in phase quadrature can result in an elevated axial ratio
(e.g., above 3 dB) at corresponding radiation frequencies.
Consequently, it is preferable to reduce the effect of transition
points to the extent practical. As will be discussed below in
additional detail, one approach to minimizing the effects of
transitions between groups of loops is to provide extrapolated
loops. Such extrapolated loops serve to make the transition between
groups more gradual.
FIG. 7A shows a further example of a polygonal spiral antenna 700
prepared according to principles of the invention including
extrapolated loops that moderate the effect of inter-group
transitions. As illustrated, antenna 700 has two spiral arms 702,
704 of 16 turns each. The spiral arms are supported by a substrate
member 706 having a substantially planar support surface. As
previously discussed, the substrate member 706 typically includes
materials having a substantially insulating or semiconducting
characteristic, and is backed by an absorbing device 710.
The spiral arms 702, 704 have respective original ends 712, 714 and
terminal ends 716, 718. Between the respective original ends 712,
714 and terminal ends 716, 718, each spiral arm describes a
generally polygonal spiral wherein radially adjacent loops of one
arm are disposed substantially co-axial to one another about
centerpoint 720. As previously noted, the loops on antenna 700 may
be grouped according to polygonal configuration, e.g., groups 722
and 724.
Antenna 700 includes first 726 and second 728 exemplary
interpolated loops between groups 722 and 724. In the context of
antenna 700, the term interpolated indicates that the loops are
modified at every last turn of each set of n-sided polygons. In the
illustrated embodiment, each arm of the spiral antenna consists of
16 turns with 4 turns of n-sided polygons. Here, each 4 turns are
such that instead of a regular n-sided polygon, the 4.sup.th turn
is an n-sided polygon interpolated from an n-sided to an
(n-1)-sided polygon. The arrangement of the interpolated loops is
more clearly seen in FIG. 7B which shows a geometric curve 730
corresponding to one arm of antenna 700. The curve includes a first
group of loops 732 and a second group of loops at 734.
Viewing curve 730 along a radially outward orientation along the
spiral, an exemplary transition point 736 is found where the curve
continues along a linear segment 738 to vertex 740, rather than
having a vertex at transition point 736. It should be noted that
vertex 740 is not disposed at location 742, and that curve 730
therefore differs from exemplary curve 610 of FIG. 6. Instead,
vertex 740 is disposed partway between transition point 736 and
location 742. Consequently, the spiral does not immediately
transition from an octagonal loop to a square loop, but forms a
further irregular octagonal loop having sides, e.g. 744, 746, that
differ in length.
In the illustrated curve 730, vertex 740 is disposed substantially
halfway between transition point 736 and location 742. This
location is particularly advantageous, although other intermediate
locations are possible and fall within the scope of the invention.
Because vertex 740 falls partway between transition point 736 and
location 742, the loop 748 is referred to as an interpolated loop
(i.e., between the loops of group 734 and the loops of group 732).
As noted above, interpolated loops tend to improve the axial ratio
performance of the antenna.
Characteristically, portions of the interpolated loop traverse what
would otherwise be open gap between groups of loops, thus
diminishing the size of such open gaps. The consequent smaller
gaps, e.g. 750, 752, result in an antenna having improved
complementarity.
While curve 730 has a single interpolated loop 748, it will be
evident in light of the present disclosure that additional
interpolated loops may be provided within the scope of the
invention. An example of an antenna including additional
interpolated loops is discussed below with respect to FIGS. 8A and
8B.
FIG. 8A shows a further example of a polygonal spiral antenna 800
prepared according to principles of the invention, including
extrapolated loops that moderate the effect of inter-group
transitions. As illustrated, antenna 800 has two spiral arms 802,
804 of 16 turns each. The spiral arms are supported by a substrate
member 806 having a substantially planar support surface. As
previously discussed, the substrate member 806 typically includes
materials having a substantially insulating or semiconducting
characteristic, and is backed by an optional absorbing device
810.
The spiral arms of antenna 800 have first interpolated loops 812
and second interpolated loops 814. These interpolated loops are
more clearly seen on FIG. 8B.
FIG. 8B shows a geometric curve 830 corresponding to one arm of
antenna 800. The curve includes a first group of loops 832, a
second group of loops 834, and a third group of loops 836. A first
interpolated loop 838 includes a transition point 840 and is
disposed between group 834 and group 832. A second interpolated
loop 842 includes a transition point 844 and is disposed between
group 836 and group 834.
As with antenna 700, each arm of antenna 800 has a single
interpolated loop, e.g., 812 between adjacent groups. In light of
the present disclosure, however, one of skill in the art will
appreciate that other arrangements are possible and fall within the
scope of the invention. Such arrangements may include, for example,
multiple loops of similar interpolation, and/or loops exhibiting
further interpolation. FIG. 9A shows one of many possible
arrangements exemplifying this possibility.
FIG. 9A shows a further example of a polygonal spiral antenna 900
prepared according to principles of the invention, including
extrapolated loops that moderate the effect of inter-group
transitions. As illustrated, antenna 900 has two spiral arms 902,
904 of 16 turns each. The spiral arms are supported by a substrate
member 906 having a substantially planar support surface. As
previously discussed, the substrate member 906 typically includes
materials having a substantially insulating or semiconducting
characteristic, and is backed by an optional absorbing device
910.
FIG. 9B shows a geometric curve 930 corresponding to one arm of
antenna device 900. The curve includes a first group of loops 932,
a second group of loops 934, a third group of loops 936, and a
fourth group of loops 940. The loops of group 932 are
non-interpolated square polygonal loops within the meaning of the
present application. Consequently exemplary vertices 940, 942 and
944 are substantially radially aligned along an axis 946 through
centerpoint 948.
In contrast, exemplary group 934 includes a plurality of loops 950,
952, 954 and 956 that are progressively interpolated between loop
956 and loop 950. This progressive interpolation corresponds to a
ratio between a long side of the loop and a short side of the loop
becoming progressively larger as one moves outward from loop to
loop across the group. Correspondingly, a radial axis 958 through
centerpoint 948 and vertex 960 of loop 952 is disposed at an angle
halfway between radial axis 962, which intersects centerpoint 948
and vertex 964 of loop 956 and radial axis 966, which intersects
centerpoint 948 and corner vertex 968. Similarly, radial axis 970
(through centerpoint 948 and vertex 972 of loop 954) is disposed at
an angle bisecting the angle between radial axes 962 and 958.
Likewise, radial axis 974 (through centerpoint 948 and vertex 976
of loop 950) is disposed at an angle bisecting the angle between
radial axes 958 and 968.
Again, it should be noted that the substantially equal angular
displacement between axes 962, 970, 958, 974 and 968 are merely
exemplary of certain desirable embodiments, and alternative
spacings and arrangements clearly fall within the scope of the
invention. It also merits notice that each of exemplary vertices
980, 982, 984, 986 and 988 are substantially aligned 990 while each
of exemplary vertices 992, 994, 996, 998 and 990 are also
substantially aligned 999.
In antenna device 900, the loops of groups 936 and 938 are
progressively interpolated, in the fashion described above with
respect to group 934. The resulting polygonal curves of antenna 900
consequently change relatively smoothly from loop the loop and
polygonal form to polygonal form between the original ends and
terminal ends of each loop. As a further consequent of these smooth
transitions the interstitial gaps e.g., 920 are relatively small as
compared with the corresponding gap of an un-interpolated antenna
(e.g., 344 of FIG. 3A).
In a further embodiment of the invention, an antenna device may
include a combination of substantially polygonal loops and smoothly
curved loops. That is, for example, substantially circular spiral
loops would be provided inwardly of, and, e.g., in series
connection with, the previously discussed substantially polygonal
loops.
Having reviewed the foregoing disclosure, the practitioner of
ordinary skill in the art will appreciate that the scope of the
present invention is not limited to antenna devices having a square
perimeter. Rather, the approaches and methods disclosed above
suggest and allow a wide variety of combinations of polygonal forms
in respective antennas according to the requirements and objectives
of a particular application. Moreover, these approaches and methods
allow for the combination of polygonal antennas according to the
present invention in antenna arrays having new and beneficial
arrangements.
FIG. 10 shows a plurality of curves representing a portion of one
such array 1000 of antenna elements. Of course array 1000 is in
tended to be exemplary of many other possibilities. As shown in
FIG. 10, for example, a plurality of polygonal antenna members
1002, 1004, 1006, 1008, each having a substantially octagonal
perimeter can be readily combined with a further antenna member
1010 having a substantially square perimeter to produce an antenna
array having an efficient packing density. Likewise other
geometries that would be understood given the benefit of the
disclosure above, including geometries having different bases and
exponents, are intended to fall within the ambit of the present
disclosure.
FIG. 11 shows, in schematic cross-section, a portion of a hybrid
spiral antenna device 1100 according to principles of the
invention. The antenna device 1100 includes a support member 1102.
In the illustrated embodiment, for example, support member 1102
includes a substantially insulating ceramic material. A
substantially planar upper surface 1104 of the support member
supports first 1106 and second 1108 hybrid polygonal spiral arms
according to principles of the invention. An absorbing device 1110,
as previously discussed, is disposed adjacent to an opposite side
of the support member 1102.
In the illustrated embodiment, the first and second hybrid
polygonal spiral arms are adapted to be driven with a
radiofrequency electrical signal at respective original ends 1112,
1114, thereof. Correspondingly, in the illustrated embodiment,
original ends 1112 and 1114 are coupled to respective conductors
1116, 1118 of a coupling device 1120. In the illustrated
embodiment, the coupling device is shown as a coaxial conducting
device having a substantially insulating dielectric material 1122
disposed between the conductors 1116, 1118. It will be understood,
however, that alternative conducting arrangements will be employed
in other embodiments of the invention. For example substantially
parallel strip lines and/or tapered line impedance transformers may
be employed.
In the embodiment shown, conductors 1116, and 1118 are coupled at
further ends 1124, 1126 to an impedance transformer 1128 which is,
in turn, coupled to a further coaxial cable 1130. In the
illustrated embodiment, the impedance transformer device serves to
match an impedance of cable 1130 of approximately 50 ohms to an
impedance of the antenna of approximately 188 ohms. In one
embodiment, the impedance transformer device includes a balun
device. In another embodiment of the invention, the impedance
transformer includes a tapered line device.
The practitioner of ordinary skill in the art will be aware of a
variety of manufacturing methods appropriate to the manufacturing
of an antenna according to principles of the invention. For
example, the antenna may be manufactured by providing an insulating
substrate, such as, e.g., a ceramic substrate, having a generally
planar upper surface. A layer of metallic material, such as copper,
is deposited on the upper surface. A photoresist is deposited on an
outer surface of the copper material. The photoresist layer is
imaged and developed to provide a layer of the photoresist having a
geometry corresponding to the desired antenna. An etching process
removes excess copper material leaving behind the desired
substantially polygonal spiral arms supported by the substrate.
Also shown is an exemplary terminating impedance 1132 coupled to a
distal end of one of the substantially polygonal spiral arms. In
still other embodiments of the invention, the antenna is driven by
the application of a radiofrequency signal to respective distal
ends of the antenna device.
Experimental Results
Gain
The full-wave analysis of the shallow cavity-backed modified
Archimedean polygonal spiral antenna has been carried out with
method-of-moments (MoM) based FEKO analysis. FEKO is a software
product developed by EM Software & Systems--S.A. (Pty) Ltd. for
the simulation of electromagnetic fields. The name is derived from
a German acronym which can be translated as "Field Calculations for
Bodies with Arbitrary Surface".
The initial simulations presented below assume matched conditions
at the antenna input port. The excitation source impedance is
defined to be 188.OMEGA. in accordance with Babinet-Booker's
principle. Table 1, below, shows the boresight co-polarized Right
Hand Circularly Polarized (RHCP) gain and the cross-polarized Left
Hand Circularly Polarized (LHCP) gain for all frequency points at 1
GHz intervals for a 2-18 GHz antenna. The antenna demonstrates
sufficiently high and stable gains, low side-lobes and no splits in
the main beam across the bandwidth.
TABLE-US-00001 TABLE 1 Right-Hand Circular Polarization and
Left-Hand Circular Polarization Gain (dB) at Boresight FREQ. GAIN
(dB) (GHz) RHC LHC 2 -1.94 -16.4 3 0.80 -18.6 4 3.29 -12.4 5 4.51
-10.1 6 5.08 -9.9 7 6.07 -20.9 8 6.49 -17.5 9 6.27 -25.8 10 5.75
-28.8 11 5.77 -23.9 12 5.58 -20.0 13 5.24 -22.1 14 5.51 -28.0 15
4.92 -24.3 16 5.05 -35.0 17 5.26 -42.5 18 5.41 -30.7
Axial Ratio
FIG. 12 shows a plot of axial ratio performance for a polygonal
spiral antenna like that of FIG. 2. As is evident from FIG. 11, the
axial ratio remains below 3 dB for 93.75% of the 2-18 GHz
bandwidth. This performance represents a significant improvement
over any previous Ultra-Wideband rectangular spiral antenna known
to the inventors.
Voltage Standing Wave Ratio (VSWR)
FIG. 13 shows the VSWR performance for an exemplary optimized
cavity-backed spiral antenna. The VSWR is referenced to 188 Ohms
and is less than 2.5:1 for the entire bandwidth of operation.
Similar characteristics could be anticipated from a well-designed
antenna according to principles of the invention.
Input Impedance
FIG. 14 shows the input impedance to the cavity-backed Archimedean
spiral antenna. The antenna realizes a near constant input
impedance structure over an ultra-wide bandwidth. The input
impedance is sensitive to small geometrical variations and slight
deviations from mean input impedance of 215.OMEGA. can be
attributed to the polygonal structure of the antenna which is not
exactly self-complementary at the transition points from 2.sup.n to
2.sup.n-1 sides.
S11
FIG. 15 shows the reflection coefficient at the antenna input port
assuming matched conditions for the simulated antenna. The results
show that the reflection coefficient is efficiently minimized to
adequate levels across the bandwidth.
Performance Comparison of Polygonal Spiral with Circular and Square
Spiral
A comparison of the radiation performance of a two-inch diameter
shallow cavity-backed polygonal spiral antenna with two-inch
circular spiral and a two-inch square spiral antenna. The results
show that the polygonal antenna offers a significantly improved
axial ratio characteristic while maintaining a gain-bandwidth
performance substantially equivalent to either of a circular spiral
and a square spiral. Table 2 illustrates a performance comparison
between a polygonal spiral and a circular spiral from 2-18 GHz at 1
GHz intervals. Table 3 illustrates a performance comparison between
a polygonal spiral and a square spiral from 2-18 GHz at 2 GHz
intervals. It is evident that circular spirals operate with better
axial ratio than square counterparts, and for equal diameters, the
polygonal spiral has the best axial ratio performance of the three
configurations.
TABLE-US-00002 TABLE 2 Boresight RHC and Gain, Axial Ratio, S11,
VSWR, and Impedance Comparison of Polygonal and Circular Spiral
Antenna AXIAL Input GAIN (dB) RATIO Impedance FREQ. RHC LHC (dB)
S11 (dB) VSWR (.OMEGA.) (GHz) Circ. Poly. Circ. Poly. Circ. Poly.
Circ. Poly. Circ. Poly. Circ. Po- ly. 2 -2.22 -1.94 -7.26 -16.4
11.00 3.33 -6.73 -7.45 2.71 2.47 70.3 191 3 1.22 0.80 -12.7 -18.6
-3.57 1.88 -13.9 -16.6 1.50 1.34 128 187 4 3.84 3.29 -8.53 -12.4
4.26 2.89 -13.9 -27.9 1.50 1.08 127 182 5 5.56 4.51 -7.02 -10.1
4.16 3.28 -12.1 -21.7 1.65 1.18 115 205 6 6.37 5.08 -19.8 -9.9 0.86
3.13 -13.7 -19.0 1.52 1.25 124 217 7 6.58 6.07 -32.5 -20.9 0.19
0.78 -13.2 -19.8 1.56 1.23 121 217 8 6.52 6.49 -36.0 -17.5 0.13
1.10 -13.9 -16.8 1.50 1.34 125 210 9 6.04 6.27 -40.9 -25.8 0.08
0.44 -14.2 -16.1 1.48 1.37 127 217 10 5.24 5.75 -52.3 -28.8 0.02
0.33 -12.6 -15.6 1.61 1.40 117 218 11 4.09 5.77 -49.2 -23.9 0.04
0.57 -9.08 -14.9 2.08 1.44 91.7 219 12 4.01 5.58 -50.2 -20.0 0.03
0.91 -9.81 -14.2 1.95 1.49 97 222 13 4.55 5.24 -54.5 -22.1 0.02
0.75 -10.1 -13.7 1.90 1.52 101 224 14 4.96 5.51 -48.8 -28.0 0.04
0.37 -10.6 -13.0 1.83 1.58 105 227 15 5.15 4.92 -53.3 -24.3 0.02
0.60 -11.0 -12.4 1.79 1.63 106 231 16 5.46 5.05 -57.0 -35.0 0.01
0.17 -11.6 -11.8 1.72 1.69 110 236 17 5.58 5.26 -86.5 -42.5 0.00
0.07 -11.8 -11.2 1.69 1.76 111 241 18 5.66 5.41 -64.9 -30.7 0.01
0.27 -12.5 -10.8 1.62 1.81 117 246
TABLE-US-00003 TABLE 3 Boresight RHC and LHC Gain, Axial Ratio,
S11, VSWR, and Impedance Comparison of a Polygonal and Square
Spiral Antenna AXIAL Input GAIN (dB) RATIO Impedance FREQ. RHC LHC
(dB) S11 (dB) VSWR (.OMEGA.) (GHz) Sqr. Poly. Sqr. Poly. Sqr. Poly.
Sqr. Poly. Sqr. Poly. Sqr. Poly. 2 -1.54 -1.94 -18.1 -16.4 2.59
3.33 -28.1 -7.45 1.08 2.47 201 191 4 3.23 3.29 -13.3 -12.4 2.6 2.89
-25.8 -27.9 1.11 1.08 208 182 6 5.53 5.08 -8.97 -9.9 3.31 3.13
-28.4 -19.0 1.08 1.25 203 217 8 6.23 6.49 -5.11 -17.5 4.83 1.10
-22.6 -16.8 1.16 1.34 204 210 10 5.51 5.75 -5.63 -28.8 4.95 0.33
-23.9 -15.6 1.14 1.40 211 218 12 4.19 5.58 -5.36 -20.0 6.01 0.91
-24.9 -14.2 1.12 1.49 207 222 14 5.05 5.51 -4.73 -28.0 5.85 0.37
-21 -13.0 1.20 1.58 214 227 16 5.84 5.05 -3.86 -35.0 5.9 0.17 -18.9
-11.8 1.26 1.69 219 236 18 4.82 5.41 -7.04 -30.7 4.53 0.27 -18
-10.8 1.29 1.81 221 246
Performance Analysis of Polygonal Spiral at Lower Frequencies
To verify the axial ratio performance of the polygonal spiral
antenna at lower frequencies, the inventors simulated the model
from 2-4 GHz at 100 MHz intervals and compared the axial ratio to
that of a circular spiral. Table 4 illustrates a performance
comparison between a polygonal spiral and a circular spiral from
2-4 GHz at 0.1 GHz intervals. The polygonal spiral shows greater
than 3 dB axial ratio at frequency interval 2.0-2.4 GHz and in the
vicinity of 3.3 GHz. The reason for the axial ratio degradation at
particular discrete frequencies can be best understood from a
heuristic approach and explained in terms of the current band
theory.
TABLE-US-00004 TABLE 4 Boresight RHC Gain, LHC Gain, Axial Ratio,
S11, VSWR, and Impedance Comparison of a Polygonal and Circular
Spiral Antenna at Low Frequencies AXIAL Input GAIN (dB) RATIO
Impedance FREQ. RHC LHC (dB) S11 (dB) VSWR (.OMEGA.) (GHz) Circ.
Poly. Circ. Poly. Circ. Poly. Circ. Poly. Circ. Poly. Circ. Po- ly.
2 -2.220 -1.96 -7.26 -16.5 11.00 3.29 -6.73 -7.42 2.71 2.48 70.3
192 2.1 -0.867 -1.19 -9.35 -13.9 6.88 4.10 -10.8 -13.8 1.81 1.51
109 270 2.2 -0.261 -1.04 -12.0 -13.4 4.61 4.29 -13.5 -18.0 1.53
1.29 125 238 2.3 0.001 -1.57 -14.1 -11.6 3.48 5.68 -14.5 -11.0 1.46
1.78 129 314 2.4 0.109 -0.60 -14.9 -14.3 3.11 3.63 -15.1 -16.4 1.43
1.36 132 139 2.5 0.152 -0.52 -14.9 -14.5 3.11 3.51 -15.0 -11.5 1.43
1.73 132 189 2.6 0.277 -0.203 -14.4 -18.9 3.25 2.02 -13.9 -13.5
1.50 1.53 126 264 2.7 0.571 0.025 -13.6 -19.1 3.46 1.92 -12.8 -15.6
1.60 1.40 118 261 2.8 0.843 0.229 -13.0 -19.8 3.59 1.73 -12.4 -17.3
1.63 1.31 115 210 2.9 0.985 0.581 -12.8 -20.0 3.61 1.63 -12.7 -20.9
1.60 1.20 118 157 3.0 1.220 0.756 -12.7 -18.8 3.56 1.84 -14.1 -17.2
1.49 1.32 127 189 3.1 1.680 0.961 -11.8 -16.2 3.73 2.41 -15.7 -16.4
1.39 1.36 135 240 3.2 1.99 1.25 -11.0 -16.8 3.98 2.19 -15.8 -17.4
1.39 1.31 136 246 3.3 2.04 1.31 -10.8 -11.9 4.01 3.87 -14.0 -20.9
1.50 1.20 128 194 3.4 2.27 1.67 -10.8 -14.1 3.91 2.86 -12.5 -21.7
1.62 1.18 117 164 3.5 2.64 1.86 -10.0 -17.3 4.12 1.92 -12.0 -21.2
1.67 1.19 113 191 3.6 2.82 2.23 -9.48 -13.8 4.30 2.76 -12.5 -22.1
1.63 1.17 116 202 3.7 3.12 2.48 -9.50 -14.7 4.14 2.42 -14.3 -19.5
1.48 1.24 130 219 3.8 3.56 2.72 -8.93 -17.3 4.20 1.74 -15.4 -23.3
1.41 1.19 135 208 3.9 3.72 2.95 -8.33 -14.4 4.43 2.36 -15.1 -21.6
1.42 1.44 132 201 4.0 3.79 3.17 -8.56 -12.6 4.27 2.88 -13.0 -23.4
1.58 1.15 119 192
Analysis of Axial Ratio Performance of Polygonal Spiral Antenna
A performance simulation based on characteristics identified with
an antenna embodying principles of the invention suggests that such
an antenna would have an axial ratio above about 3 dB at discrete
frequencies 2.1-2.5 GHz and at 3.3 GHz. This phenomenon can be
attributed to the fact that the current wavelengths corresponding
to these frequencies are located at the transition points of the
polygonal geometry.
FIG. 16 illustrates, in graphical schematic form, the results of a
simulation indicating current distributions in adjacent arms when
the antenna is operating at 2.3 GHz. Specifically, FIG. 16 shows a
portion of a polygonal spiral antenna 1600. Antenna 1600 includes a
first group of loops 1602 and a second group of loops, 1604 and a
transition point 1606. In a region inward of the transition point,
which is to say relatively circumferentially proximate to a driven
end of the antenna (e.g., original ends of the antenna arms), first
1108 and second 1110 currents are in phase. Conversely, in a region
outward of the transition point 1606, corresponding currents are
out of phase, 1112, 1114.
Polygonal Spiral Antenna with 12.sup.th Interpolated Turn
Further simulation results suggest that axial ratios above 3 dB may
be anticipated at discrete frequencies 2.1-2.5 GHz and at 3.3 GHz.
This phenomenon can be attributed to the fact that the current
wavelengths corresponding to these frequencies are located at the
transition points of the polygonal geometry. A simulation was
performed with respect to an antenna similar to that of FIG. 7A. In
this simulation a 12th turn of the spiral is modified such that
instead of a regular octagon, the spiral arm includes an octagon
interpolated from an 8 sided to a 4 sided polygon. The purpose of
this modification is to allow for a smoother transition and reduce
the axial ratio at a 2.1-2.5 GHz range. The antenna model and the
corresponding spiral curve are shown in FIGS. 7A and 7B
respectively.
Performance Comparison of Polygonal Spiral with Circular Spiral
Table 5 illustrates a performance simulation comparing a polygonal
spiral antenna according to principles of the invention and a
circular spiral antenna over a frequency range from 2-18 GHz at 1
GHz intervals.
TABLE-US-00005 TABLE 5 Boresight RHC Gain, LHC Gain, Axial Ratio,
S11, VSWR, and Impedance Comparison of a Polygonal and Circular
Spiral Antenna AXIAL Input GAIN (dB) RATIO Impedance FREQ. RHC LHC
(dB) S11 (dB) VSWR (.OMEGA.) (GHz) Circ. Poly. Circ. Poly. Circ.
Poly. Circ. Poly. Circ. Poly. Circ. Po- ly. 2 -2.22 -1.46 -7.26
-14.0 11.00 4.16 -6.73 -11.735 2.71 1.70 70.3 288 3 1.22 0.77 -12.7
-16.1 -3.57 2.51 -13.9 -21.942 1.50 1.18 128 193 4 3.84 2.97 -8.53
-13.6 4.26 2.59 -13.9 -18.579 1.50 2.06 127 233 5 5.56 4.35 -7.02
-18.7 4.16 1.22 -12.1 -20.362 1.65 1.67 115 209 6 6.37 5.33 -19.8
-9.03 0.86 3.36 -13.7 -20.022 1.52 1.22 124 221 7 6.58 6.31 -32.5
-19.1 0.19 0.94 -13.2 -20.164 1.56 1.71 121 210 8 6.52 6.29 -36.0
-31.5 0.13 0.22 -13.9 -17.195 1.50 1.32 125 216 9 6.04 6.66 -40.9
-30.8 0.08 0.23 -14.2 -16.98 1.48 1.33 127 216 10 5.24 6.16 -52.3
-36.9 0.02 0.12 -12.6 -16.18 1.61 1.37 117 218 11 4.09 6.00 -49.2
-28.6 0.04 0.32 -9.08 -15.29 2.08 1.42 91.7 221 12 4.01 5.57 -50.2
-23.0 0.03 0.65 -9.81 -14.65 1.95 1.45 97 223 13 4.55 5.17 -54.5
-30.8 0.02 0.28 -10.1 -14.09 1.90 1.49 101 225 14 4.96 4.90 -48.8
-33.7 0.04 0.20 -10.6 -13.38 1.83 1.55 105 227 15 5.15 4.91 -53.3
-39.7 0.02 0.10 -11.0 -12.82 1.79 1.59 106 230 16 5.46 5.25 -57.0
-32.3 0.01 0.23 -11.6 -12.12 1.72 1.66 110 236 17 5.58 5.33 -86.5
-25.8 0.00 0.48 -11.8 -11.54 1.69 1.72 111 240 18 5.66 8.82 -64.9
-23.5 0.01 0.62 -12.5 -11.30 1.62 1.75 117 243
Performance Analysis of Polygonal Spiral at Lower Frequencies
To verify the axial ratio performance of the polygonal spiral
antenna at lower frequencies, a model of an antenna according to
principles of the invention was simulated over frequency ranges
from 2-4 GHz and 5-7 GHz at 100 MHz intervals. Table 6 illustrates
the performance comparison of a polygonal spiral and a circular
spiral from 2-4 GHz at 0.1 GHz intervals. The polygonal spiral
shows less than 3 dB axial ratio at frequency intervals of 2.0-2.23
GHz, 5.9-6.2 GHz and in the vicinity of 5.4 and 3.5 GHz.
TABLE-US-00006 TABLE 6 Boresight RHC Gain, LHC Gain, Axial Ratio,
S11, VSWR, and Impedance Comparison of a Polygonal and Circular
Spiral Antenna at Low Frequencies AXIAL Input GAIN (dB) RATIO
Impedance FREQ. RHC LHC (dB) S11 (dB) VSWR (.OMEGA.) (GHz) Circ.
Poly. Circ. Poly. Circ. Poly. Circ. Poly. Circ. Poly. Circ. Po- ly.
2 -2.220 -1.46 -7.26 -14.0 11.00 4.16 -6.73 -11.74 2.71 1.70 70.3
288 2.1 -0.867 -1.32 -9.35 -13.5 6.88 4.34 -10.8 -14.27 1.81 1.48
109 237 2.2 -0.261 -1.15 -12.0 -13.9 4.61 4.06 -13.5 -13.72 1.53
1.52 125 148 2.3 0.001 -0.71 -14.1 -17.0 3.48 2.69 -14.6 -14.32
1.46 1.48 129 229 2.4 0.109 -0.52 -14.9 -16.6 3.11 2.73 -15.1
-14.03 1.43 1.50 132 260 2.5 0.152 -0.45 -14.9 -22.2 3.11 1.42
-15.0 -13.94 1.43 1.50 132 270 2.6 0.277 -0.09 -14.4 -25.6 3.25
0.92 -13.9 -18.69 1.50 1.26 126 167 2.7 0.571 0.09 -13.6 -22.7 3.46
1.26 -12.8 -17.03 1.60 1.33 118 175 2.8 0.843 0.01 -13.0 -21.7 3.59
1.53 -12.4 -15.22 1.63 1.42 115 244 2.9 0.985 0.41 -12.8 -16.9 3.61
2.40 -12.7 -15.36 1.60 1.41 118 265 3.0 1.220 0.77 -12.7 -16.1 3.56
2.51 -14.1 -21.94 1.49 1.17 127 193 3.1 1.680 0.98 -11.8 -15.6 3.73
2.60 -15.7 -24.13 1.39 1.08 135 173 3.2 1.99 1.23 -11.0 -16.0 3.98
2.41 -15.8 -22.64 1.39 1.16 136 197 3.3 2.04 1.31 -10.8 -15.4 4.01
2.56 -14.0 -18.34 1.50 1.27 128 217 3.4 2.27 1.81 -10.8 -15.3 3.91
2.44 -12.5 -23.10 1.62 1.15 117 214 3.5 2.64 1.79 -10.0 -12.0 4.12
3.60 -12.0 -20.29 1.67 1.21 113 218 3.6 2.82 2.36 -9.48 -15.4 4.30
2.26 -12.5 -24.97 1.63 1.12 116 199 3.7 3.12 2.45 -9.50 -20.15 4.14
1.29 -14.3 -19.54 1.48 1.24 130 200 3.8 3.56 2.68 -8.93 -12.9 4.20
2.90 -15.4 -20.57 1.41 1.21 135 214 3.9 3.72 2.96 -8.33 -14.0 4.43
2.47 -15.1 -18.96 1.42 1.25 132 215 4.0 3.79 2.97 -8.56 -13.62 4.27
2.59 -13.0 -18.58 1.58 1.27 119 233 5.0 5.56 4.35 -7.02 -18.7 4.16
1.22 -12.1 -20.362 1.65 1.67 115 209 5.1 5.02 4.38 -7.70 -21.2 4.09
0.91 -8.94 -22.97 2.11 1.15 93 206 5.2 5.27 4.74 -7.67 -13.4 4.05
2.15 -7.93 -24.68 2.34 1.12 94 193 5.3 5.24 4.73 -7.57 -11.6 3.73
2.67 -7.93 -18.47 2.36 1.27 98 198 5.4 5.66 4.74 -8.25 -10.5 3.51
3.03 -9.24 -19.48 2.04 1.24 110 213 5.5 5.99 4.77 -8.35 -9.80 3.37
3.54 -12.0 -16.80 1.67 1.34 134 210 5.6 6.11 4.93 -8.35 -12.1 2.82
2.45 -14.74 -18.08 1.45 1.29 157 232 5.7 6.35 5.19 -9.75 -23.0 2.31
0.68 -16.96 -22.24 1.33 1.17 172 209 5.8 6.38 5.18 -11.37 -16.0
1.37 1.53 -19.83 -19.44 1.22 1.24 176 200 5.9 6.48 5.29 -15.76
-9.81 1.03 3.13 -23.88 -16.47 1.14 1.35 173 226 6.0 6.55 5.33
-18.02 -9.04 1.04 3.36 -24.61 -20.02 1.13 1.22 167 221 6.1 6.52
5.48 -17.90 -9.49 0.41 1.13 -19.7 -19.10 1.23 1.25 158 209 6.2 6.55
5.63 -26.06 -11.7 0.46 2.37 -16.54 -17.69 1.35 1.30 148 228 6.3
6.51 5.74 -24.98 -19.5 0.46 0.95 -14.76 -21.08 1.45 1.54 139 217
6.4 6.48 5.78 -25.01 -15.7 0.35 1.47 -13.57 -22.30 1.54 1.16 130
202 6.5 6.42 5.84 -27.52 -13.0 0.35 2.00 -12.46 -18.38 1.62 1.27
121 210 6.6 6.41 6.09 -27.12 -14.2 0.36 1.69 -11.57 -19.74 1.72
1.23 113 218 6.7 6.40 6.17 -30.91 -16.9 0.24 1.22 -11.14 -20.35
1.77 1.21 109 204 6.8 6.42 6.13 -28.84 -19.8 0.30 0.88 -10.91
-18.24 1.80 1.28 106 211 6.9 6.38 6.21 -35.30 -20.6 0.14 0.79
-10.71 -18.44 1.82 1.27 103 218 7.0 6.39 6.31 -31.27 -19.1 0.23
0.94 -10.56 -20.16 1.84 1.22 102 210
Performance Comparison of Polygonal Spiral with Circular Spiral
Table 7 illustrates a performance simulation comparing a polygonal
spiral antenna according to principles of the invention and a
circular spiral antenna over a frequency range from 2-18 GHz at 1
GHz intervals.
TABLE-US-00007 TABLE 7 Boresight RHC Gain, LHC Gain, Axial Ratio,
S11, VSWR, and Impedance Comparison of a Polygonal and Circular
Spiral Antenna AXIAL Input GAIN (dB) RATIO Impedance FREQ. RHC LHC
(dB) S11 (dB) VSWR (.OMEGA.) (GHz) Circ. Poly. Circ. Poly. Circ.
Poly. Circ. Poly. Circ. Poly. Circ. Po- ly. 2 -2.22 -2.12 -7.26
-15.2 11.00 3.90 -6.73 -7.47 2.71 2.47 70.3 334 3 1.22 0.81 -12.7
-18.4 3.56 1.91 -14.1 -16.35 1.49 2.66 127 194 4 3.79 3.30 -8.56
-18.0 4.27 1.50 -13.0 -22.67 1.58 1.16 119 213 5 5.47 4.41 -6.94
-9.34 4.05 3.62 -11.4 -29.55 1.54 1.07 125 190 6 6.55 5.30 -18.02
-11.2 1.04 2.62 -24.61 -18.66 1.13 1.26 167 183 7 6.58 6.18 -32.5
-12.7 0.19 1.98 -13.2 -18.08 1.56 1.29 121 202 8 6.52 6.22 -36.0
-20.8 0.13 0.77 -13.9 -16.90 1.50 1.33 125 211 9 6.04 6.16 -40.9
-24.7 0.08 0.50 -14.2 -16.28 1.48 1.36 127 211 10 5.24 6.27 -52.3
-21.1 0.02 0.74 -12.6 -15.19 1.61 1.42 117 213 11 4.09 5.70 -49.2
-24.3 0.04 0.55 -9.08 -14.50 2.08 1.46 91.7 218 12 4.01 5.61 -50.2
-26.1 0.03 0.45 -9.81 -13.88 1.95 1.51 97 220 13 4.55 5.40 -54.5
-21.3 0.02 0.81 -10.1 -13.20 1.90 1.56 101 224 14 4.96 4.91 -48.8
-26.4 0.04 0.46 -10.6 -12.59 1.83 1.61 105 226 15 5.15 4.77 -53.3
-40.3 0.02 0.10 -11.0 -11.88 1.79 1.68 106 231 16 5.46 4.98 -57.0
-31.3 0.01 0.27 -11.6 -11.31 1.72 1.75 110 236 17 5.58 5.18 -86.5
-26.3 0.00 0.46 -11.8 -10.79 1.69 1.81 111 242 18 5.66 5.28 -64.9
-31.5 0.01 0.25 -12.5 -10.33 1.62 1.88 117 247
Performance Analysis of Polygonal Spiral at Lower Frequencies
A further simulation was performed with respect to a polygonal
spiral antenna at lower frequencies. This simulation modeled the
subject device over a frequency range of 2-6 GHz at 100 MHz
intervals. Table 8 illustrates a performance simulation comparing a
polygonal spiral and a circular spiral over frequency range of 2-6
GHz at 0.1 GHz intervals. The simulation suggests polygonal spiral
antenna performance with an axial ratio above 3 dB at frequency
intervals 2.0-2.6 GHz, 4.8-5.1 GHz and in the vicinity of 3.8
GHz.
TABLE-US-00008 TABLE 8 Boresight RHC Gain, LHC Gain, Axial Ratio,
S11, VSWR, and Impedance Comparison of a Polygonal and Circular
Spiral Antenna at Low Frequencies AXIAL Input GAIN (dB) RATIO
Impedance FREQ. RHC LHC (dB) S11 (dB) VSWR (.OMEGA.) (GHz) Circ.
Poly. Circ. Poly. Circ. Poly. Circ. Poly. Circ. Poly. Circ. Po- ly.
2 -2.22 -2.12 -7.26 -15.2 11.00 3.90 -6.73 -7.47 2.71 2.47 70.3 334
2.1 -0.87 -2.17 -9.35 -15.5 6.88 3.83 -10.8 -7.44 1.81 2.48 109 352
2.2 -0.26 -0.92 -12.0 -14.0 4.61 3.93 -13.5 -23.83 1.53 1.12 125
213 2.3 0.00 -0.62 -14.1 -14.0 3.48 3.79 -14.5 -17.44 1.46 2.10 129
149 2.4 0.11 -0.72 -14.9 -16.6 3.11 2.82 -15.1 -13.11 1.43 1.57 132
209 2.5 0.15 -0.65 -14.9 -14.6 3.11 3.52 -15.0 -13.18 1.43 1.56 132
292 2.6 0.28 0.01 -14.4 -21.9 3.25 1.73 -13.9 -24.63 1.50 1.17 126
213 2.7 0.57 0.20 -13.6 -18.2 3.46 2.09 -12.8 -24.63 1.60 1.12 118
211 2.8 0.84 0.35 -13.0 -21.5 3.59 1.40 -12.4 -27.66 1.63 1.09 115
180 2.9 0.99 0.65 -12.8 -31.0 3.61 0.46 -12.7 -20.80 1.60 1.20 118
166 3.0 1.22 0.81 -12.7 -18.4 3.56 1.91 -14.1 -16.35 1.49 2.66 127
194 3.1 1.68 0.98 -11.8 -17.0 3.73 2.21 -15.7 -16.85 1.39 1.34 135
228 3.2 1.99 1.27 -11.0 -16.0 3.98 2.41 -15.8 -17.99 1.39 1.29 136
239 3.3 2.04 1.53 -10.8 -14.6 4.01 2.74 -14.0 -24.56 1.50 1.13 128
207 3.4 2.27 1.76 -10.8 -14.5 3.91 2.69 -12.5 -24.17 1.62 1.13 117
173 3.5 2.64 2.03 -10.0 -14.6 4.12 2.58 -12.0 -19.30 1.67 1.24 113
192 3.6 2.82 2.31 -9.48 -15.0 4.30 2.39 -12.5 -19.45 1.63 1.24 116
195 3.7 3.12 2.41 -9.50 -16.0 4.14 2.09 -14.3 -17.01 1.48 1.33 130
217 3.8 3.56 2.77 -8.93 -10.6 4.20 3.77 -15.4 -21.60 1.41 1.18 135
204 3.9 3.72 2.92 -8.33 -13.7 4.43 2.59 -15.1 -21.80 1.42 1.42 132
208 4.0 3.79 3.30 -8.56 -18.0 4.27 1.50 -13.0 -22.67 1.58 1.16 119
213 4.1 3.75 3.45 -8.26 -12.5 4.27 2.80 -11.7 -25.72 1.74 1.11 109
194 4.2 3.94 3.66 -8.41 -12.4 4.24 2.78 -14.1 -19.90 1.70 1.22 111
213 4.3 4.43 3.88 -7.97 -13.2 4.44 2.46 -15.6 -22.23 1.49 1.17 127
211 4.4 4.62 3.88 -7.41 -13.2 4.29 2.46 -12.9 -22.23 1.40 1.17 135
211 4.5 4.62 4.16 -7.70 -17.9 4.21 1.38 -11.2 -18.84 1.59 1.26 122
225 4.6 4.81 4.10 -7.67 -13.1 4.37 2.42 -11.4 -25.57 1.76 1.11 108
200 4.7 4.94 4.34 -7.23 -13.5 4.22 2.24 -13.4 -21.74 1.74 1.18 108
215 4.8 5.14 4.38 -7.32 -10.7 4.13 3.10 -15.1 -25.35 1.54 1.11 123
195 4.9 5.48 4.22 -7.17 -9.18 4.24 3.77 -13.4 -22.14 1.42 1.17 132
210 5.0 5.47 4.41 -6.94 -9.34 4.05 3.62 -11.4 -29.55 1.54 1.07 125
190 5.1 5.02 4.40 -7.70 -8.94 4.09 3.80 -8.94 -19.49 2.11 1.24 111
191 5.2 5.27 4.54 -7.67 -11.2 4.05 2.87 -7.93 -18.85 2.34 1.99 94
215 5.3 5.24 4.75 -7.57 -12.3 3.73 2.46 -7.93 -23.77 2.36 1.14 98
200 5.4 5.66 4.84 -8.25 -10.9 3.51 2.85 -9.24 -22.03 2.04 1.17 110
206 5.5 5.99 4.87 -8.35 -10.5 3.37 2.99 -12.0 -23.73 1.67 1.14 134
184 5.6 6.11 4.87 -8.35 -11.4 2.82 2.68 -14.74 -17.46 1.45 1.31 157
191 5.7 6.35 4.95 -9.75 -13.1 2.31 2.17 -16.96 -17.15 1.33 1.32 172
217 5.8 6.38 5.18 -11.37 -29.8 1.37 0.31 -19.83 -32.23 1.22 1.22
176 213 5.9 6.48 5.30 -15.76 -15.0 1.03 1.68 -23.88 -24.09 1.14
1.13 173 196 6.0 6.55 5.30 -18.02 -11.2 1.04 2.62 -24.61 -18.66
1.13 1.26 167 183
Polygonal Spiral Antenna with Gradually Transitioning Arms
A further simulation was performed with respect to a polygonal
spiral antenna with gradually transitioning arms. In this model of
the polygonal spiral antenna, each arm of the spiral antenna
consists of 16 turns with sets of 4 turns of n-sided polygons.
However, each 4 turns are such that the first turn is a regular
n-sided polygon with n-equal sides, then the consecutive turns are
n-sided polygons gradually transitioning from an n-sided to an
(n-1)-sided polygon. The simulated antenna is similar to that of
FIGS. 9A and 9B.
Performance Comparison of Polygonal Spiral with Circular Spiral
Table 9 illustrates a performance comparison between a polygonal
spiral and a circular spiral over a frequency range from about 2-18
GHz at 1 GHz intervals.
TABLE-US-00009 TABLE 9 Boresight RHC Gain, LHC Gain, Axial Ratio,
S11, VSWR, and Impedance Comparison of a Polygonal and Circular
Spiral Antenna AXIAL Input GAIN (dB) RATIO Impedance FREQ. RHC LHC
(dB) S11 (dB) VSWR (.OMEGA.) (GHz) Circ. Poly. Circ. Poly. Circ.
Poly. Circ. Poly. Circ. Poly. Circ. Po- ly. 2 -2.220 -1.49 -7.26
-16.9 11.00 2.97 -6.73 -13.87 2.71 1.51 70.3 152 3 1.220 0.83 -12.7
-16.8 3.56 2.29 -14.1 -21.85 1.49 1.18 127 221 4 3.79 3.21 -8.56
-13.9 4.27 2.44 -13.0 -22.63 1.58 1.16 119 211 5 5.47 4.28 -6.94
-8.4 4.05 4.12 -11.4 -17.40 1.54 1.31 125 199 6 6.55 5.26 -18.02
-13.2 1.04 2.09 -24.61 -16.17 1.13 1.37 167 209 7 6.58 6.01 -32.5
-10.6 0.19 2.59 -13.2 -16.18 1.36 1.37 121 205 8 6.52 6.19 -36.0
-12.3 0.13 2.08 -13.9 -14.52 1.50 1.46 125 228 9 6.04 6.02 -40.9
-21.3 0.08 0.75 -14.2 -14.32 1.48 1.48 127 220 10 5.24 5.94 -52.3
-21.2 0.02 0.77 -12.6 -14.19 1.61 1.48 117 221 11 4.09 5.93 -49.2
-26.1 0.04 0.44 -9.08 -13.24 2.08 1.56 91.7 224 12 4.01 5.44 -50.2
-22.8 0.03 0.68 -9.81 -12.65 1.95 1.60 97 226 13 4.55 5.17 -54.5
-37.3 0.02 0.13 -10.1 -11.84 1.90 1.69 101 232 14 4.96 4.89 -48.8
-19.5 0.04 1.05 -10.6 -11.30 1.83 1.75 105 236 15 5.15 4.89 -53.3
-37.6 0.02 0.13 -11.0 -10.63 1.79 1.83 106 243 16 5.46 4.81 -57.0
-26.4 0.01 0.48 -11.6 -10.03 1.72 1.92 110 249 17 5.58 4.96 -86.5
-28.1 0.00 0.39 -11.8 -9.55 1.69 2.00 111 257 18 5.66 3.15 -64.9
-28.6 0.01 0.36 -12.5 -9.14 1.62 2.07 117 264
Performance Analysis of Polygonal Spiral at Lower Frequencies
To verify the axial ratio performance of the polygonal spiral
antenna at lower frequencies, a further simulation was performed
representing an antenna having characteristics according to the
invention. This simulation was performed over a frequency range
from about 2-6 GHz at 100 MHz intervals. Table 10 illustrates a
simulated performance comparison between a polygonal spiral antenna
and a circular spiral over a frequency range from about 2-6 GHz at
0.1 GHz intervals. The results of the simulation suggest a
polygonal spiral having an axial ratio above 3 dB at frequency
intervals from about 4.9-5.0 GHz, 5.3-5.7 GHz, and in the vicinity
of 2.1 GHz.
TABLE-US-00010 TABLE 10 Boresight RHC Gain, LHC Gain, Axial Ratio,
S11, VSWR, and Impedance Comparison of a Polygonal and Circular
Spiral Antenna at Low Frequencies AXIAL Input GAIN (dB) RATIO
Impedance FREQ. RHC LHC (dB) S11 (dB) VSWR (.OMEGA.) (GHz) Circ.
Poly. Circ. Poly. Circ. Poly. Circ. Poly. Circ. Poly. Circ. Po- ly.
2 -2.220 -1.49 -7.26 -16.9 11.00 2.97 -6.73 -13.87 2.71 1.51 70.3
152 2.1 -0.867 -1.47 -9.35 -16.6 6.88 3.09 -10.8 -15.48 1.81 1.40
109 139 2.2 -0.261 -1.08 -12.0 -16.3 4.61 2.98 -13.5 -16.72 1.53
1.34 125 194 2.3 0.001 -0.68 -14.1 -16.3 3.48 2.90 -14.5 -30.11
1.46 1.06 129 200 2.4 0.109 -0.76 -14.9 -16.3 3.11 2.94 -15.1
-16.56 1.43 1.35 132 142 2.5 0.152 -0.84 -14.9 -16.6 3.11 2.87
-15.0 -11.39 1.43 1.74 132 188 2.6 0.277 -0.42 -14.4 -17.2 3.25
2.54 -13.9 -10.80 1.50 1.81 126 310 2.7 0.571 -0.12 -13.6 -17.1
3.46 2.48 -12.8 -13.63 1.60 1.53 118 269 2.8 0.843 0.15 -13.0 -17.1
3.59 2.39 -12.4 -21.82 1.63 1.41 115 183 2.9 0.985 0.65 -12.8 -17.5
3.61 2.16 -12.7 -27.11 1.60 1.09 118 194 3.0 1.220 0.83 -12.7 -16.8
3.56 2.29 -14.1 -21.85 1.49 3.18 127 221 3.1 1.680 1.02 -11.8 -16.6
3.73 2.30 -15.7 -26.17 1.39 1.10 135 184 3.2 1.99 1.41 -11.0 -17.5
3.98 1.97 -15.8 -24.68 1.39 1.12 136 169 3.3 2.04 1.48 -10.8 -17.7
4.01 1.91 -14.0 -18.35 1.50 1.27 128 171 3.4 2.27 1.69 -10.8 -16.4
3.91 2.17 -12.5 -17.11 1.62 1.32 117 203 3.5 2.64 2.14 -10.0 -15.7
4.12 2.25 -12.0 -18.70 1.67 1.26 113 207 3.6 2.82 2.20 -9.48 -16.0
4.30 2.14 -12.5 -18.61 1.63 1.26 116 217 3.7 3.12 2.58 -9.50 -16.1
4.14 2.02 -14.3 -19.87 1.48 1.22 130 213 3.8 3.56 2.68 -8.93 -17.0
4.20 1.81 -15.4 -19.65 1.41 1.23 135 209 3.9 3.72 2.90 -8.33 -15.0
4.43 2.23 -15.1 -18.49 1.42 1.27 132 230 4.0 3.79 3.21 -8.56 -13.9
4.27 2.44 -13.0 -22.63 1.58 1.16 119 211 4.1 3.75 3.39 -8.26 -12.7
4.27 2.75 -11.7 -20.29 1.74 1.21 109 218 4.2 3.94 3.65 -8.41 -12.4
4.24 2.75 -14.1 -23.78 1.70 1.14 111 212 4.3 4.43 3.71 -7.97 -12.7
4.44 2.65 -15.6 -25.61 1.49 1.11 127 207 4.4 4.62 3.98 -7.41 -13.4
4.29 2.37 -12.9 -22.20 1.40 1.17 135 186 4.5 4.62 4.15 -7.70 -12.8
4.21 2.50 -11.2 -19.53 1.59 1.24 122 203 4.6 4.81 4.18 -7.67 -15.6
4.37 1.78 -11.4 -20.39 1.76 1.21 108 196 4.7 4.94 4.22 -7.23 -23.3
4.22 0.74 -13.4 -21.98 1.74 1.17 108 199 4.8 5.14 4.25 -7.32 -11.3
4.13 2.92 -15.1 -16.33 1.54 1.36 123 208 4.9 5.48 4.25 -7.17 -7.8
4.24 4.34 -13.4 -21.57 1.42 1.18 132 213 5.0 5.47 4.28 -6.94 -8.4
4.05 4.12 -11.4 -17.40 1.54 1.31 125 199 5.1 5.02 4.64 -7.70 -11.4
4.09 2.76 -8.94 -19.24 2.11 1.25 93 216 5.2 5.27 4.61 -7.67 -11.4
4.05 2.76 -7.93 -17.11 2.34 1.32 94 215 5.3 5.24 4.75 -7.57 -10.3
3.73 3.10 -7.93 -18.87 2.36 1.26 98 226 5.4 5.66 4.79 -8.25 -9.96
3.51 3.22 -9.24 -24.46 2.04 1.13 110 196 5.5 5.99 4.84 -8.35 -9.27
3.37 3.47 -12.0 -18.12 1.67 1.28 334 199 5.6 6.11 4.81 -8.35 -8.22
2.82 3.94 -14.74 -19.20 1.45 1.25 157 210 5.7 6.35 4.97 -9.75 -10.3
2.31 3.03 -16.96 -18.70 1.33 1.26 172 216 5.8 6.38 5.17 -11.37
-12.0 1.37 2.43 -19.83 -23.29 1.22 1.15 176 193 5.9 6.48 5.24
-15.76 -12.8 1.03 2.19 -23.88 -17.47 1.14 1.31 173 188 6.0 6.55
5.26 -18.02 -13.2 1.04 2.09 -24.61 -16.17 1.13 1.37 167 209
As previously noted, devices prepared according to principles of
the invention offer the opportunity to produce electromagnetic
radiation with an axial ratio under 3 dB for 93%-99% of its
bandwidth, depending on the particular embodiment or device, while
preserving the advantages of a square spiral antenna. The radiation
patterns obtained from the proposed polygonal geometry are compared
to that obtained from purely circular and purely square patterns
having the same diameter and the significant improvement in axial
ratio is demonstrated in the results. Having the benefit of the
present disclosure, one of skill in the art will readily develop
further modifications, variants and derivatives of the disclosed
geometries and devices exhibiting performance and characteristics
beneficially applied to any number of related applications.
Simulations of further embodiments suggest that the inventive
antenna device can readily produce 3 dB axial ratios at discrete
frequencies 2.1-2.5 GHz and at 3.3 GHz. This phenomenon can be
attributed to the fact that the current wavelengths corresponding
to these frequencies are located at the transition points of the
polygonal geometry. As noted above, FIG. 16 illustrates current
distributions in adjacent loops when the antenna is operating at
2.3 GHz.
FIG. 17 shows, in sectional perspective view, a portion of a
further antenna device 1700 prepared according to principles of the
invention. Like the devices described above, the antenna device
1700 includes a plurality of turns, the turns including a first
turn having a first polygonal spiral configuration and a further
turn having a second polygonal spiral configuration. For example,
the illustrated device 1700, includes a first substantially square
polygonal spiral turn 1702 and a further substantially octagonal
polygonal spiral turn 1704. The further turn 1704 is disposed
radially inward of the first turn 1702. As shown, the antenna
device 1700 also includes turns that are offset along an axis 1706
that is disposed normal to a plane defined by the further turn
1704. The result is an antenna device 1700 having a generally
polygonal generally helical spiral configuration.
FIG. 18 shows a further embodiment in which an antenna 1800
includes a plurality of groups e.g., 1802, 1804, 1806 of
substantially polygonal spiral loops. The loops within each group
are generally coplanar with one another. The groups are offset from
one another along a longitudinal axis 1808. The loops of each group
respectively are signalingly coupled in series with one another,
and the groups are likewise coupled in series 1810, 1812. One of
skill in the art will appreciate that the representation of FIG. 18
is schematic and contains only exemplary portions of the
represented antenna. Various practical implementations may include
a larger number of groups, and may incorporate other features
described in relation to the previously identified embodiments such
as, for example, interpolated loops.
It should also be noted that, while the foregoing description has
referred primarily to spirals which are generally Archimedean in
form, other configurations of spirals are also considered to be
within the scope of the invention.
In a further aspect, the invention includes a method of preparing
an antenna device having polygonal spiral loops as described above.
In certain aspects, such a method includes using a computer device
or computer system to define a plurality of generally polygonal
generally spiral geometric curves. Thereafter, these curves may be
implemented as a physical antenna by, for example, photochemical
etching, computer-aided routing, three-dimensional printing, wire
bending, or any other appropriate manufacturing means. The
exemplary code below will provide to the practitioner of ordinary
skill in the art the understanding necessary to readily implement
such a method.
TABLE-US-00011 //Code for drawing the geometric spiral curves:
//Function for drawing close loop polygons and determining the
//relationship etween the angles //maximum sides of polygons
#define MAXSIDES 32 // how many turns at each number of sides
#define TURNSPER 4 // how many steps (32, 16, 8, 4) ---> 4 steps
#define NUMSTEPS 4 #define PI 3.14159 // numsides -- how many sides
// ratio of 1.0 means a regular n-gon, 0.0 makes regular n/2-gon //
buffer is where to put results, r1,theta1,r2,theta2.... void
make_poly(int numSides,double ratio,double *buffer){ double
shortAngle; double longAngle; int i; double r; double theta;
shortAngle = ratio*2*PI/((double)numSides); longAngle = (2*PI -
(numSides/2)shortAngle)/((double)numSides/2); r =
1.0/cos(longAngle/2.0); theta = longAngle/2.0; for(i = 0;i <
numSides;i++){ buffer[2*i] = r; buffer[2*i +1] = theta; if(i%2 ==
0){ theta += shortAngle; } else{ theta += longAngle; } } return; }
// Main program for original polygonal spiral int main(int argc,
char **argv){ int i; double ratio; int j; double
buffer[2*MAXSIDES]; int sides = MAXSIDES; int k; double r; double
theta; double angleSoFar; // 2*pi*(number of turns completed)
double radiusPerRadian = 2.0/(NUMSTEPS*TURNSPER*2*PI); double x,y;
for(i = 0;i < NUMSTEPS;i++){ for(j =0;j < TURNSPER;j++){
make_poly(sides, 1.0,buffer); } //at this point, buffer contains
polar coords for // vertices of a sides-son of width 1. Need to
scale it // to the proper width for the spiral, then convert to //
cartesian coords for(k = 0;k < sides;k++){ // unpack coordinates
from the buffer r = buffer[2*k]; theta = buffer[2*k+1]; r *=
radiusPerRadian*(angleSoFar + theta); x = r*cos(theta); y =
r*sin(theta); printf("%f %f\n",x,y); } angleSoFar += 2*PI; } sides
/=2; } return 0; } // Main program for 12.sup.th interpolated turn
int main(int argc, char **argv){ int i; double ratio; int j; double
buffer[2*MAXSIDES]; int sides = MAXSIDES; int k; double r; double
theta; double angleSoFar; // 2*pi*(number of turns completed)
double radiusPerRadian = 2.0/(NUMSTEPS*TURNSPER*2*PI); double x,y;
int flag = 0; for(i = 0;i < NUMSTEPS;i++){ for(j =0;j
<TURNSPER;j++){ if ((sides == 4) && (j == 0)){ sides =
8; flag = 1; make_poly(sides,0.5,buffer); } else{
make_poly(sides,1.0,buffer); } //at this point, buffer contains
polar coords for // vertices of a sides-gon of width 1. Need to
scale it // to the proper width for the spiral, then convert to //
cartesian coords for(k = 0; k < sides;k++){ // unpack
coordinates from the buffer r = buffer[2*k]; theta = buffer[2*k+1];
r *= radiusPerRadian*(angleSoFar + theta); x = r*cos(theta); y =
r*sin(theta); printf("%f %f\n",x,y); } if(flag){ sides = 4; }
angleSoFar += 2*PI; } sides /=2; } return 0; } // Main program for
last interpolated turns int main(int argc, char **argv){ int i;
double ratio; int j; double buffer[2*MAXSIDES]; int sides =
MAXSIDES; int k; double r; double theta; double angleSoFar; //
2*pi*(number of turns completed) double radiusPerRadian =
2.0/(NUMSTEPS*TURNSPER*2*PI); double x,y; for(i = 0;i <
NUMSTEPS;i++){ for(j =0;j < TURNSPER;j++){ if((sides > 4)
&& (j == (TURNSPER - 1))){ make_poly(sides,0.5,buffer); }
else{ make_poly(sides,1.0,buffer); } //at this point, buffer
contains polar coords for // vertices of a sides-gon of width 1.
Need to scale it // to the proper width for the spiral, then
convert to // cartesian coords for(k = 0;k < sides;k++){ //
unpack coordinates from the buffer r = buffer[2*k]; theta =
buffer[2*k+1]; r *= radiusPerRadian*(angleSoFar + theta); x =
r*cos(theta); y = r*sin(theta); printf("%f %f\n",x,y); } angleSoFar
+= 2*PI; } sides /=2; } return 0; } // Main program for gradually
transitioning arms int main(int argc, char **argv){ int i; double
ratio; int j; double buffer[2*MAXSIDES]; int sides = MAXSIDES; int
k; double r; double theta; double angleSoFar; // 2*pi*(number of
turns completed) double radiusPerRadian =
2.0/(NUMSTEPS*TURNSPER*2*PI); double x,y; for(i = 0;i <
NUMSTEPS;i++){ for(j =0;j < TURNSPER;j++){ if(sides > 4){
make_poly(sides,((double)(4-j))/4.0,buffer); } else{
make_poly(sides,1.0,buffer); } //at this point, buffer contains
polar coords for // vertices of a sides-gon of width 1. Need to
scale it // to the proper width for the spiral, then convert to //
cartesian coords for(k = 0;k < sides;k++){ // unpack coordinates
from the buffer r = buffer[2*k]; theta = buffer[2*k+1]; r *=
radiusPerRadian*(angleSoFar + theta); x = r*cos(theta); y =
r*sin(theta); printf("%f %f\n",x,y); } angleSoFar += 2*PI; } sides
/= 2; } return 0; }
An exemplary embodiment of a practical antenna is fabricated on
Rogers Type RT5880 Duroid substrate that is 0.02 inches thick. The
substrate is copper-clad on both sides, therefore the copper was
etched off the back side. This substrate is chosen because it
provides the closest permittivity match (.di-elect cons.r=2.20) to
air from 2-18 GHz. A 0.06 inch-diameter spacing was used at the
feed-points at the center of the antenna structure. The cavity
depth is 0.625 inch including the air-gap between the radiator and
the absorbing layers.
The antenna is fed in unbalanced co-axial mode from the back of the
cavity. A wideband tapered coaxial balun is used that transforms
the unbalanced coaxial mode into a balanced two-wire transmission
line mode that feeds the spiral antenna. The balun also allows for
impedance transformation from the 50.OMEGA. impedance of the
coaxial line to the impedance of the spiral antenna.
In the design of the balun, the antenna impedance is assumed to be
188 Ohms and to be connected to a 50 Ohm connector. The unbalanced
balun is used to feed the antenna with one of its sides grounded to
the connector and the other side connected to the center pin of the
connector. Using a tapered transmission line design, the grounded
side of the balun is tapered until it becomes balanced and then the
split ends of the tapered coax balun are soldered to the antenna.
Where the total cavity depth is 0.625 inches, the balun height is
0.675 inches. Extra length 0.05 inches is added to allow for
soldering the balun to the antenna arms. Similar baluns used for
cavity-backed spirals operating at 2-18 GHz are found in commercial
models.
While the exemplary embodiments described above have been chosen
primarily from the field of radio communication, one of skill in
the art will appreciate that the principles of the invention are
equally well applied, and that the benefits of the present
invention are equally well realized in a wide variety of other
applications including, for example, product identification and
tracking, material processing, aerospace communications, commercial
and defense satellites, GPS systems, microwave direction finding
systems and other applications that previously have been used, as
well as other systems involving the application of electromagnetic
fields and radiation.
Further, while the invention has been described in detail in
connection with the presently preferred embodiments, it should be
readily understood that the invention is not limited to such
disclosed embodiments. Rather, the invention can be modified to
incorporate any number of variations, alterations, substitutions,
or equivalent arrangements not heretofore described, but which are
commensurate with the spirit and scope of the invention.
Accordingly, the invention is not to be seen as limited by the
foregoing description, but is only limited by the scope of the
appended claims.
* * * * *
References